Bayern Munich, already crowned champions, followed up their memorable midweek thrashing of Barcelona by setting a Bundesliga points record with a 1-0 win over Freiburg on Saturday.
Bayern's probable Champions League final opponents Borussia Dortmund beat Fortuna Dusseldorf 2-1 with the help of a stunning Nuri Sahin goal.
Werder Bremen were sucked closer to the danger zone after losing 1-0 to a controversial penalty at third-placed Bayer Leverkusen, leaving them only two points clear of the relegation play-off place after Augsburg beat VfB Stuttgart 3-0.
Augsburg's win meant bottom club Greuther Furth, making their Bundesliga debut this season, were relegated. Furth lost 3-2 at home to Hannover 96 on Friday.
Xherdan Shaqiri's first-half free-kick put treble-chasing Bayern on 84 points, three more than the previous record set by Dortmund last season, with three games to play.
The Bavarians made 10 changes from the team that started Tuesday's 4-0 Champions League semi-final first leg win over Barcelona and clocked up their 27th victory in 31 league games, improving their goal difference to 76.
Swiss winger Shaqiri continued his impressive debut season at Bayern by curling in a free-kick for the only goal against fifth-placed Freiburg, the surprise package of the campaign.
It was Bayern's 14th successive league win although the single goal was something of a letdown for a team that had blasted 20 in their last four matches in all competitions.
"What [coach] Christian Streich has achieved in Freiburg is sensational," said Bayern coach Jupp Heynckes. "A lot of things have come together there over a period of years.
"It was a hard job of work today but credit to the lads. We were very smart and very professional."
Second-placed Dortmund, who thumped Real Madrid 4-1 on Wednesday, also made 10 changes and went ahead when Sahin scored with a curving, dipping left-foot shot from 35 metres after 20 minutes.
Sahin also laid on the second goal for Jakub Blaszczykowski in the 70th before Dortmund, 20 points behind Bayern, had to survive a late fightback by Fortuna with Adam Bodzek heading home two minutes from time.
Fortuna are fourth from bottom on 30 points, ahead of Augsburg on goal difference.
Sascha Molders, Marcel de Jong and South Korean Ji Dong-Won scored in the last half hour for third-bottom Augsburg.
Second-bottom Hoffenheim beat Nuremberg 2-1 to stay three points behind Augsburg.
Tobias Weis and Sejad Salihovic scored in the first 19 minutes for Hoffenheim and Timmy Simons replied with a second-half penalty.
VfL Wolfsburg defeated Borussia Monchengladbach 3-1 after 18-year-old Maximilian Arnold opened the scoring with his third goal in five appearances.
The real surprise is the presence of four-times champions Werder Bremen, who extended their sequence without a win to 10 games, among the strugglers.
They lost in controversial circumstances when goalkeeper Sebastian Mielitz was judged to have fouled Sidney Sam in the 35th minute.
Sam was sent clean through and flicked his shot wide but the onrushing Mielitz clattered into him after the ball had gone.
The keeper appeared to spread himself deliberately and raised his foot and the referee pointed to the spot after consulting the linesman.
Stefan Kiessling, repeatedly overlooked by Germany coach Joachim Low despite his consistent scoring, converted the penalty for his 22nd league goal this season although Mielitz got a hand to it.
"When you put down rules they should be the same, week in, week out," said Werder coach Thomas Schaaf. "I can't understand the decision, every referee seems to have his own rulebook."